81.7.2 problem 3

Internal problem ID [18699]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:10:44 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} x^{2} y^{\prime \prime }&=\ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(x^2*diff(y(x),x$2)=ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (x \right )-\frac {\ln \left (x \right )^{2}}{2}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 24

DSolve[x^2*D[y[x],{x,2}]==Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{2} \log ^2(x)-\log (x)+c_2 x+c_1 \]